Computation of Lebesgue’s Space-Filling Curve
Journal Title: Computer Reviews Journal - Year 2019, Vol 4, Issue 0
Abstract
The means of realizing or approximating the Lebesgue space-filling curve (SFC) with binary arithmetic on a uniformly spaced binary grid are not obvious, one problem being its formulation in terms of ternary representations; that impediment can be overcome via use of a binary-oriented Cantor set. A second impediment, namely the Devil’s Staircase feature, also created by the role of the Cantor set, can be overcome via the definition of a “working inverse”, thereby providing means of achieving compatibility with such a grid. The results indicate an alternative way to proceed, in realizing an approximation to Lebesgue’s SFC, which circumvents any complication raised by Cantor sets and is compatible with binary and integer arithmetic. Well-known constructions such as the z-curve or Morton order, sometimes considered in association with Lebesgue’s SFC, are treated as irrelevant.
Authors and Affiliations
Arthur R Butz
Keywords
Related Articles
- EP ID EP655232
- DOI -
- Views 125
- Downloads 0
Close-up Macro and Micro Photogrammetry and Image Perspective: A Comparative Studio on different Lenses at work with Small and Medium Size Object
The digital photogrammetry has renewed the approach to measurement for archaeologists, architects and many researchers, students, professionals in Cultural Heritage. Thus, most of the troubles coming from the more and mo...
Cross-Layer Design of Dynamic Link Prediction Power Control Algorithm in Wireless Ad hoc Networks
In wireless communication era, Dynamic Link Prediction based Cross-Layer Power Control Algorithm (DLP-CLPCA) in wireless ad hoc networks provides a joint solution for the power consumption protocol as well as nodes link...
Search Engine Search Engine Search Engine Optimization with Google Search Console
This paper is based on how Google search engine optimization effectively works. And the visibility and quality content of the search engine index page. The keyword feature targeted in this paper is to follow Google quali...
A Study of The Application Of Simulation Software for Business Processes
This paper reports on the experiences of using two popular business process simulation (BPS) software packages. BPS is a technique, which assists companies in mimicking their everyday operations to find ways in which to...
A General Study on Langevin Equations of Arbitrary Order
In this paper, the broad study depends on Langevin differential equations (LDE) of arbitrary order. The fractional order is in terms of ψ-Hilfer fractional operator. This work reveals the dynamical behaviour such as exis...